Question

In a survey it was found that $21$ people liked product A, $26$ liked product B and $29$ liked product C. If $14$ people liked products A and B, $12$ people liked products C and A, $14$ people liked products B and C and $8$ liked all the three products.
Find how many liked product C only

Answer 1

Let A, B, and C be the set of people who like product A, product B, and product C respectively.

Accordingly, $n\left(A\right)=21,n\left(B\right)=26,n\left(C\right)=29,n(A\cap B)=14,n(C\cap A)=12,n(B\cap C)=14,n(A\cap B\cap C)=8$

The Venn diagram for the given problem can be drawn as above.

It can be seen that number of people who like product C only is
$\{29-(4+8+6\left)\right\}=11$